Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets - Muoi, Bui Ngoc; Wong, Ngai-Ching (Topological Methods in Nonlinear Analysis, 2022)
Let S be a right reversible semitopological semigroup, and let LUC(S) be the space of left uniformly continuous functions on S. Suppose that LUC(S) has a left invariant mean. Let K be a weakly compact convex subset of a Banach space not necessarily with normal structure. We show that there always exists a common fixed point for any jointly weakly continuous and super asymptotically nonexpansive action of S on K. Several variances involving the weak* compactness, the RNP, the distality of K and/or the left reversibility of S are also provided.